When Eduardo Andreu recently informed someone that he is Icelandair's representative in Orlando, that person responded, ''Oh. That's the new air- conditioning shop.''

Accustomed to such comments, Andreu sometimes describes Icelandair as ''the airline that no one has ever heard of that flies from Orlando to a country no one has heard of.''

Last fall, Icelandair became the first airline to fly regularly between Orlando and a foreign country. That country is not Iceland but Luxembourg, which is wedged between Belgium, France and Germany.

Despite its identity problem, Iceland- air is thriving on its new route, according to Andreu.

The airline recently added a second weekly flight between Orlando and Luxembourg and is considering adding two more weekly flights in 1986. All flights became nonstop Sunday. Before, they stopped in Baltimore. Most flights are more than 85 percent full, Andreu said.

Round-trip fares ranging from $499 to $699 provide Floridians with some of the least-expensive regularly scheduled flights to Europe.

Icelandair's Orlando-Luxembourg route is attracting travelers from North and West Florida as well as Orlando area residents. Earlier this month, the airline began providing free bus service between Orlando International Airport and Clearwater, St. Petersburg and Tampa.

''We're getting some business from South Florida but not as much as we expected,'' Andreu said. Icelandair is negotiating a joint-fare agreement with a U.S. airline to bring passengers from Miami to Orlando.

Although a newcomer to Florida, Icelandair is a veteran in flying across the Atlantic.

The airline, which is based in Reykjavik, Iceland, began flying regularly between New York and Luxembourg in 1955. In some of its promotional brochures, Icelandair says it is a pioneer in providing inexpensive flights between the United States and Europe. The airline also notes that it preceded Sir Freddie Laker and the former Laker Airways in this endeavor.

''That's the first airline I ever took to Europe,'' Marilyn Wright, an Orlando area travel agent, recalled. At that time, in 1966, she was a student at Florida State University in Tallahassee and Icelandair was the least- expensive way to reach Europe from New York, she said.

Because Icelandair transported so many U.S. college students, such as Wright, and young travelers, to Europe during the 1960s, it was called ''the hippie airline.''

''They've remained very competitive in price,'' Wright said. ''They have excellent vacation packages.''

Icelandair's vacation packages scheduled later this year include skiing trips to Kitzbuhel, Austria. Air fare, a car, lodging and some meals will cost $619 for one week and $749 for two weeks.

The airline also offers a Luxembourg fly-and-drive package that provides rental cars for $59 a week. ''That's cheaper than you can rent a car in Florida,'' Andreu said.

Besides featuring low prices, Icelandair's vacation packages often highlight special themes. For example, the airline offered ''designer shopping sprees to Paris'' early this year and a tour of World War II battle sites last fall.

Icelandair fares better when the U.S. dollar is weak in relation to foreign currencies, said Einar Gustavsson, a regional sales manager in New York.

The airline collects about 45 percent of its revenue in dollars but pays about 65 percent of its expenses in dollars, he said. When the dollar is strong as it is now, ''we take a big beating on converting European currencies,'' Gustavsson said.

Despite that, Icelandair has been profitable during most of its history, he said. The airline reported a profit of $11 million and revenue of $120 million for 1984. That compares with a profit of $5 million and revenue of $106 million in 1983.

The airline transported 707,000 travelers last year, almost triple Iceland's population of 245,000. About 24,000 travelers will be transported to and from Orlando this year, Gustavsson predicted.

A stop in Iceland may be included in one of the Orlando-Luxembourg flights to be added next year, Gustavsson said. Such a stop would enable travelers to change planes to visit the airline's Scandinavian destinations -- Bergen, Copenhagen, Gothenburg, Oslo and Stockholm. From Iceland, travelers also can use Icelandair to fly to Glasgow, Scotland; Salzburg, Austria; London; Greenland and the Faroe Islands.

From 1968 until 1981, Icelandair operated Air Bahama, which offered inexpensive flights between Nassau and Luxembourg. The airline suspended that service when Europe's economy began to deteriorate.

The airline's current network contrasts with its humble beginnings.

A U.S. Army Air Force aircraft abandoned on a glacier in Iceland provided some entreprenuers there with the money to expand their struggling airline. They dug the DC-3 from snow and ice in 1951, towed it away on dog sleds, refurbished it and sold it to the Spanish government for $44,000.

Since then, Icelandair has grown to employ 1,600 people, including 130 in the United States. Its fleet of 20 aircraft includes nine jets. The airline's owners include the Icelandic government, Icelandic Steamship Co. and about 3,500 individuals.

Icelandair is able to be profitable and offer inexpensive fares because it fills its flights, Gustavsson said. In addition, Andreu said, employees are trained to perform many tasks -- called ''cross-utilization'' in the airline industry.

Cross-utilization, a strategy now being implemented by U.S. airlines, has been used by Icelandair for decades, he said. The airline's lone full-time employee in Florida, Andreu is responsible for advertising and sales, and he helps passengers at Orlando International Airport.